Machine learning interatomic potentials (MLIPs) are moving from narrowly parameterized models toward expressive foundation models that cover much of the periodic table. In this talk I summarize this development through the lens of the Graph Atomic Cluster Expansion (GRACE). GRACE provides a formally complete basis for many-body atomic interactions and, on that basis, a unified model hierarchy: many recent MLIPs, from local descriptor-based potentials to semilocal message-passing networks, emerge as specific limits of the GRACE formalism.

The framework also brings computational advantages. GRACE avoids the combinatorial growth in basis size that usually accompanies multi-component systems, retaining linear scaling with system size while scaling favorably with the number of chemical elements and the complexity of the basis.

Finally, I present applications that span general-purpose foundation models and fine-tuned models for specific problems: predicting melting temperatures, diffusion mechanisms and barriers, and grain boundary structures, optimizing surface compositions of multi-component alloys, and simulating the reduction of iron by hydrogen. I also show how recently developed atom-resolved uncertainty estimates make it possible to detect extrapolation on the fly, so that simulations of millions of atoms can be run with confidence.